Degree reduction for trigonometric functions

Abstract

This report is a companion to Reference 1 on radian reduction. As in Reference 1, the motivation arises from a desire to eliminate messages like "argument too large" in trigonometric function routines. The presence of very large arguments in the VAX H format, on the Crayl, and on an IEEE machine with extended registers, make this a real problem. As for the radian reduction algorithm, the degree algorithm will reduce any argument, however large, so long as it is representable; its speed is nearly independent of the size of the argument to be reduced; and full accuracy is maintained in the neighborhoods of the zeros of the desired function. We believe that the approach is new and represents a significant improvement over procedures currently in use. A variant of the procedure is used in Version 3 of the VAX Math Library.